Time interval measurement is used in a wide range of applications, especially for scientific measurements where high accuracy and precision are desired. Digital time measurement is commonly used, by means of a Time-to-Digital Converter (TDC), in which a trigger signal is used to start a digital timer and the time being measured is determined using a response signal which is digitally sampled. The accuracy is therefore limited by the sampling rate of the Analogue to Digital Convertor (ADC). It is known to use interpolation methods to achieve resolutions better than the sampling rate. Examples of such methods are presented at various publications, for instance “Review of methods for time interval measurements with picoseconds resolution”, Jozef Kalisz, Metrologia 41 (2004) 17-32.
One application of such time interval measurement is in Time-of-Flight (TOF) mass spectrometry. The use of time interval measurement in such a mass spectrometer is detailed in WO-2011/048060. Here, the process of acquiring pulses which correspond with ions of different mass-to-charge (m/z) ratios is initiated either by:    a) the signal of an electronic component (such as a photodiode) produced as a response of a laser pulse, which is responsible for the desorption or ionisation of ions from a surface or for ionisation of gasses; or    b) electronic pulses which signify the extraction of ions from the ion source (such a source can be orthogonal extracting electrodes or an RF trap).
An existing time interval measurement uses two ADCs, each running with a 1 GHz clock and therefore providing samples every 1 ns. The ADC interface is configured to communicate with two parallel data buses, each running at 250 MHz with Double Data Rate (DDR) and therefore provides two samples every 2 ns. An FPGA section is connected to the ADC interface and thereby simultaneously captures 4 ADC samples every clock cycle (4 ns period). To build a correlation within the 4 GHz time domain (required for 250 ps resolution), an interpolation technique is implemented. Referring to FIG. 1, there is shown a schematic timing diagram to detail how such interpolation within a clock cycle can be implemented. The “trigger IN” event is captured and delayed by 250 ps, 500 ps and 750 ps inside the FPGA. The input signal (such as a mass spectrum) is then matched to the four delayed “trigger IN” signals. This allows a timing resolution of 250 ps to be obtained.
To demonstrate the performance of such a digitiser at 1 ns sampling rate and the effect of interpolation, experiments were carried out. These will now be described. A Gaussian pulse was produced by a test device and subsequently fed to a first channel of a digitiser. The same test device produced a trigger pulse to cause generation of the Gaussian pulse, with the ability to delay the trigger pulse by multiples of 11 ps. The timing of the Gaussian pulse was measured 100 times for each delay of the trigger pulse.
Referring to FIG. 2, there is shown a plot of the average centroid time and the standard deviation of the centroid time for the Gaussian pulse as the delay is varied. The trigger pulse was delayed between 0 and 5000 ps. On the acquisition side, the trigger was recorded with a resolution of 1000 ps (which was the native sample rate of the ADC). The standard deviation of the centroid time is generally low. At five significant positions though, the standard deviation peaks at approximately (50% of the sample rate). The peaks have a width of about 120 ps. These large standard deviation peaks appear inevitable and can be related to the sample rate. At these positions, a transition between two samples occurs, each with a width of 1000 ps. The overall standard deviation is 290.54 ps.
To improve the detection accuracy for the trigger, interpolation circuitry was implemented. This maps the trigger to one of four 250 ps wide bins, as explained above with reference to FIG. 1. Referring to FIG. 3, there is shown a plot of the average centroid time and the standard deviation of the centroid time for the Gaussian pulse as the delay is varied for the interpolation case. In comparison with FIG. 2, it can be seen that the average centroid number of steps is increased (by a factor of 4) and the step size and step width is reduced. In practice, it is not possible to calibrate these bins to exactly 250 ps width. Therefore, the steps in the average centroid plot of FIG. 3 do not have the same width. The number of peaks in the centroid standard deviation has correspondingly increased, but the height of these peaks is lower (around 125 ps). The width of these peaks is about 100 ps and they are around 250 ps apart. The overall standard deviation for this experiment is 82.34 ps, which is only about a quarter of the overall standard deviation of the same experiment with 1000 ps trigger resolution.
This means that a resolution of approximately 250 ps is indeed possible using interpolation. However, it can be seen that calibration of the high resolution trigger is not perfect, due to hardware limitations. Higher resolution measurement without such difficulties is a continuing challenge.